Screw element for same-sense rotating multi-screw extruders

ABSTRACT

A screw element includes an outer radius R a  and a core radius R i  for multiscrew extruders with co-rotating and intermeshing screw shafts. The screw element has in axial cross section through its longitudinal axis a profile which has at each of the two axial end faces (i.e. a front end face and a rear end face) only one screw flight corresponding to a conventional single-start screw element for intermeshing screw shafts. In this case, the width (flight land angle φ) of the screw flight and conversely, in a corresponding way, the width (flight land angle φ) of the screw flight are formed in a special way and a shearing flight with a constant shearing flight radius R s , which is greater than R i , and less than R a , is provided.

PRIORITY CLAIM

This is a national stage of PCT application No. PCT/DE02/00901, filed on08 Mar. 2002. Priority is claimed on that application and on thefollowing application(s): Country: Germany, Application No.: 101 14727.9, Filed: 22 Mar. 2001.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The invention relates to a screw element with an outer radius R_(a) anda core radius R_(i) for multiscrew extruders with co-rotating andintermeshing screw shafts, in particular for twin-screw extruders, whichhas in axial cross section through its longitudinal axis a profile whichhas at each of the two axial end faces only a screw flight correspondingto a conventional single-start screw element for intermeshing screwshafts, the surface of which flight, between a left and a right flightedge, is part of a surface of a cylinder with the outer radius R_(a),each end face having a circular root with the core radius R_(i) of thescrew shaft and a left and a right flank, which joins the root to theleft and right flight edge, respectively.

2. Description of the Related Art

The design principles for creating screw elements for co-rotating andclosely meshing multiscrew extruders, which are also referred to asErdmenger profiles, have been known for many years. A correspondingdescription can be found for example in the book “DerDoppelschneckenextruder, Grundlagen und Anwendungsgebiete” [Thetwin-screw extruder, principles and areas of application], published byVDI Verlag GmbH, Dusseldorf, 1995 (pages 10-30). In the illustration 1.4(page 14) of this publication there is shown, for example, an axialcross section of the profile of a single-start screw element of the typementioned at the beginning.

For the dispersive and distributive mixing of additives, for example, orother components into plastic compositions, usually kneading blockswhich comprise a plurality of kneading disks with an Erdmenger profile,arranged axially one behind the other and offset angularly with respectto one another, are used. The kneading disks are respectively arrangedin pairs, lying opposite one another on the two screw shafts of therespective twin-screw extruder, and closely intermesh. The mixingprocess in conventional kneading blocks is to be regarded as a randomprocess, i.e. the mixing work performed in individual volume elementsvaries in intensity. Therefore, to achieve a high degree of homogeneityof the mixture, considerable mechanical energy has to be expended toensure that, as far as possible, every volume unit also undergoesshearing. On the basis of an individual kneading disk, a relativelysmall proportion of the material to be handled is in each case shearedextremely intensely, while by far the greatest part of the materialevades the shearing gap between the shearing disk and the barrel walland is consequently sheared only little. For this reason, to ensure ahigh degree of homogeneity of the mixture, either very long kneadingblocks of the known type or else high rotational speeds are required. Inany event, considerable mechanical energy is expended and is introducedin the form of heat into the material to be handled. In particularduring the processing of rubber mixes, the generation of relativelylarge amounts of heat is extremely undesirable.

DE 42 39 220 A1 discloses a twin-screw extruder with two identical,closely meshing and co-rotationally driven screw shafts, which arearranged in the bores of a shared barrel. The screw shafts are providedwith kneading disks, which have a three-start shaft cross section, thatis to say have three flight lands. The distance of the flight lands fromthe inner surface of the barrel bore and the width of the flight landsvary. The flight land with the greatest flight land width has in thiscase the smallest distance from the inner surface of the barrel bore.The screw elements known from this document are of a three-start formover their entire axial length.

SUMMARY OF THE INVENTION

The object of the present invention is to develop a screw element of thegeneric type to the extent that, with the same homogenizing result, amuch smaller amount of energy is introduced into the material to behandled.

This object is achieved according to the present invention in the caseof a screw element of the generic type by the features specified in thedefining part of patent claim 1. Advantageous developments of theinvention emerge from the dependent claims.

The screw element according to the invention has in cross sectionthrough its longitudinal axis a front and a rear end face, whichcorresponds in its shape to that of a single-start screw element forintermeshing screw shafts of multiscrew extruders. As a result, thisscrew element can be combined without any problems whatsoever withcorresponding conventional single-start screw elements for co-rotatingand intermeshing screw shafts on a shared screw shaft. The profilegeometry of the screw element is preferably designed for close meshingof the screw elements. In this case, the play between the screw elementsand the inner wall of the extruder barrel and between one another,necessary for technical production-related reasons, is usually in thedimensional range of just a few tenths of a millimeter. However, thesuccess according to the invention can also be achieved in significantpart if a greater play (in the range of up to several millimeters, forexample 1-5 mm, depending on the barrel diameter) is chosen and thescrew elements cannot touch one another, that is to say do not closelymesh in the strict sense.

To avoid misunderstandings, it should be pointed out that the followingstatements respectively relate to a pair of screws rotating to the rightin the direction of the process.

Over the axial length between the front end face and the rear end face,the shape of this screw element significantly deviates, however, fromthe known geometry of single-start screw elements, but without losingthe property of intermeshing or closely meshing. As it proceeds from thefront end face and the flight edge opposite to the rotational sense ofthe screw element (in the case of rotation to the right, that is to saystarting from the left flight edge) along the longitudinal axis up to apartial length x of the axial length l of the screw element, the widthof the screw flight (flight land angle) is reduced down to 0 to form anedge. The distance of this edge from the longitudinal axis is initiallyreduced with increasing distance from the front end face and thenincreases again, however, until this edge ends in the flight edgecorresponding to the rotational sense of the screw element (in the caseof rotation to the right, that is to say in the right flight edge) atthe rear end face. Conversely, in a corresponding way, as it proceedsfrom the rear end face and the flight edge corresponding to therotational sense (in the case of rotation to the right, that is to saythe right flight edge) along the longitudinal axis up to a partiallength x of the axial length l of the screw element, the width of thescrew flight is reduced down to 0 to form an edge, the distance of whichfrom the longitudinal axis is then initially reduced and subsequently,as the distance of the flight surface from the longitudinal axisincreases again, ends in the flight edge opposite to the rotationalsense of the screw element (in the case of rotation to the right, thatis to say the left flight edge) at the front end face. Consequently,instead of having a single flight with a constant flight width andconstant distance of the flight surface from the longitudinal axis, thisscrew element has two flight elements running symmetrically in relationto each other with respect to the longitudinal axis, which in oneportion have in each case a constant flight radius as the flight width(flight land angle) decreases and in a further portion have a flightwidth of 0 (i.e. formation of an edge) and a distance from thelongitudinal axis that varies along the longitudinal axis. In addition,however, the screw element according to the invention is alsocharacterized by a further flight, that is a shearing flight. Thisshearing flight has a shearing flight radius R_(s), i.e. a distance fromthe longitudinal axis of the screw element which is greater than thecore radius R_(i) and less than the outer radius R_(a). The shearingflight extends from that point on the flank corresponding to therotational sense of the screw element (in the case of rotation to theright, that is to say the right flank) of the front end face, which hasthe distance Rs from the longitudinal axis, and proceeds in a helicalform corresponding to the rotational sense of the screw element to theflank opposite to the rotational sense of the screw element (in the caseof rotation to the right, that is to say the left flank) of the rear endface. The shearing flight comprises in its axial length an axial middlepiece of substantially constant flight width (i.e. constant flight landangle) and in each case a transitional piece from the middle piece tothe front and rear end face, respectively. In these transitional pieces,the flight width is in each case reduced as it increasingly approachesthe end face, preferably continuously down to 0 to form an edge, whichat the respective end face ends in the flank.

The described profile of the shearing flight is in principle designedsuch that it acts in a backward-conveying sense on the material to behandled. This characteristic can be significantly influenced, however,if the shape of the screw element is superposed with an additionalpitch, at least over part of its axial length, in that the shape of thescrew element is twisted, that is to say cross sections lying one behindthe other are turned with respect to one another. On the basis of theaxial length of one portion of the screw element, the magnitude of thetwisting can, if required, be chosen differently in individual portions.To intensify the backward-conveying effect of the shearing flight, theadditional pitch can be brought about by twisting the cross section withrespect to the front end face in the direction of the intendedrotational direction of the screw element. A reduction in thebackward-conveying effect, or even reversal into an especiallyadvantageous forward-conveying effect, can be achieved by the additionalpitch being brought about by twisting the cross section with respect tothe front end face in the direction counter to the intended rotationaldirection of the screw element. This embodiment is particularlypreferred within the scope of the present invention.

The additional pitch is expediently superposed on the screw element overits entire length. It is also possible, however, to superpose differentadditional pitches on a plurality of portions of the screw element lyingaxially one behind the other.

The action of the screw element according to the invention is such thatthe material conveyed by the respective multiscrew extruder is drawninto a screw channel, that is to say into the respective cavity betweenthe screw element and the extruder barrel surrounding the screw element,which is bounded by a shearing flight in the sense of a barrier and thecross-sectional volume of which in the conveying direction is reduced to0, so that the material is forced in its entirety over the shearingflight. Consequently, a defined shearing and stretching takes place foreach volume element of the material to be handled. No specialback-pressure elements are required to ensure adequately thoroughmixing. Therefore, an extruder system equipped with the screw elementaccording to the invention can be readily run empty. Added to this isthe fact that the profile of this screw element according to theinvention is self-cleaning if it is designed as a closely meshing screwelement. On account of these properties, material changes and also colorchanges can be accomplished particularly quickly and with minimal effortin the case of an extruder system equipped with the screw elementsaccording to the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

In the drawings, wherein like reference characters denote similarelements throughout the several views:

FIG. 1 a is a perspective view from the front right of a wire model of ascrew element according to the invention;

FIG. 1 b is a perspective view from the front right of a surface modelof the screw element of a FIG. 1 a;

FIG. 2 a is a perspective view from the front left of a wire model ofthe screw element of FIG. 1 a;

FIG. 2 b is a perspective view from the front left of a surface model ofa screw element of FIG. 1 a;

FIG. 3 is a side view of a wire model of the screw element of FIG. 1 a;

FIG. 4 is a cross-sectional view of the screw element in FIG. 3 alongline IV—IV;

FIG. 5 is a cross-sectional view of the screw element in FIG. 3 alongline V—V;

FIG. 6 is a cross-sectional view of the screw element in FIG. 3 alongline VI—VI;

FIG. 7 is a cross-sectional view of the screw element in FIG. 3 alongline VII—VII;

FIG. 8 is a cross-sectional view of the screw element in FIG. 3 alongline VIII—VIII;

FIG. 9 is a cross-sectional view of the screw element in FIG. 3 alongline IX—IX;

FIG. 10 is a cross-sectional view of the screw element in FIG. 3 alongline X—X;

FIG. 11 a is a perspective view from the front left of a wire model ofanother screw element according to the invention having an additionallysuperposed pitch;

FIG. 11 b is a perspective view from the front left of a surface modelof the screw element in FIG. 11 a; and

FIG. 12 is a perspective view from right of a surface model of the screwelement of FIG. 11 a.

DETAILED DESCRIPTION OF THE PRESENTLY PREFERRED EMBODIMENTS

The screw element according to the invention, shown in FIGS. 1 and 2 ina perspective view from the front right and the front left, respectively(in FIG. 1 a and FIG. 2 a as a wire model and in FIG. 1 b and FIG. 2 bas a surface model) is intended for a right-turning screw shaft, asindicated by the thick arrow entered on the front end face 8. Theprofile of the end face 8 in the chosen exemplary embodiment is that ofa closely meshing single-start Erdmenger screw element. The longitudinalaxis 10 of the screw element has an axial length 1. Between the points5, 6, which are also referred to as flight edges, extends the flight 1,which has a surface in the form of a cylinder shell and is formed in theend section as an arc of a circle with the radius R_(a) about the centerpoint defined by the longitudinal axis 10. The flight width is definedby the flight land angle φ, which is formed between the two radii R_(a)passing through the left and right flight edges 5, 6, respectively.Diametrically opposite the flight 1 lies the root 2, which likewise hasa shape in the form of a cylinder shell and is therefore circular in endsection. The radius of the root is denoted by R_(i) and corresponds tothe core diameter of the associated screw shaft (core radius R_(i)). Inthe circumferential direction, the root 2 of the end face 8, in a waysimilar to the flight 1, extends over an angle φ. Between the flight 1and the root 2 lie two flanks 3, 4, which in the end face 8 respectivelycorrespond to an arc of a circle with the radius R_(a)+R_(i). The circlecenter point for the flank 4 lies on the opposite left flight edge 5,while the center point of the left flank 3 lies on the opposite rightflight edge 6. In principle, it is possible to choose the flight landangle φ for the flight 1 to be different from the flight land angle forthe root 2. In this case, however, the mating element meshing with therespective screw element would have to have a correspondinglycomplementary, different shape. In particular for technicalproduction-related reasons, it is recommendable to choose the two flightland angles to be the same, as in the exemplary embodiment representedaccording to FIG. 1, in order to allow in each case 2 identical screwelements to intermesh.

The rear end face 8′, lying opposite the front end face 8, has anentirely identical profile shape. To differentiate from the points orprofile lines of the front end face 8, the corresponding points andprofile lines of the rear end face 8′ are identified by the samenumbering with an additional prime, as revealed by FIGS. 1 and 2. Thelatter shows the screw element from FIG. 1 in a perspective view fromthe front left. Between the two end faces 8, 8′, the screw element hasthe following shape: in the axial direction from the front end face 8 tothe rear end face 8′, the width of the flight 1 decreases down to thevalue 0 as it proceeds from the left flight edge 5 up to an axialpartial length x. At the point of the partial length x, both flightedges 5, 6 consequently coincide to form a point and then continue in acommon edge 11, which ends in the right flight edge 6′ of the rear endface 8′. The distance of the edge 11 from the longitudinal axis 10 inthis case initially decreases over a further part of the axial lengthand then increases again up to the original value R_(a) at the point 6′.Conversely, in a corresponding way, as it proceeds from the right rearflight edge 6′ in the direction of the front end face 8, the flightwidth 1′ decreases to the value 0 by the time it reaches an axialpartial length x. There, the two flight edges 6′ and 5′ again coincideat a point and continue in an edge 11′ until the left flight edge 5 inthe front end face 8 is reached. The edge 11′ has a profilecorresponding to the edge 11, that is to say, as it increasinglyapproaches the end face 8, it initially reduces its distance from thelongitudinal axis 10, starting from the original value R_(a), over acertain part of the axial length and, after that, increases again up tothe original value R_(a). In addition to the two flight elements similarto each other in the form of the flight 1 and the edge 11 or the flight1′ and the edge 11′, the screw element according to the invention alsohas a third flight element in the form of a shearing flight 7, whichextends at a constant distance (shearing flight radius R_(s)) from thelongitudinal axis 10 as it proceeds from the right flank 4 at the frontend face 8 in the direction of rotation intended for the screw elementaccording to the invention (that is to say right-rotating here) up to acorresponding point 9′ on the left flank 3′ at the rear end face 8′. Theflight width (measured as the shearing flight land angle from thelongitudinal axis 10, not represented in FIGS. 1 and 2) is constant in amiddle portion of the axial length l. However, the latter is notabsolutely necessary. Between the front end face 8 and the rear end face8′, the middle piece of the shearing flight 7 respectively continues ina transitional piece up to the two end faces 8, 8′. In this transitionalpiece, the distance (shearing flight radius R_(s)) from the longitudinalaxis 10 remains constant in each case. As it proceeds from therespective end face 8, 8′, the shearing flight 7 initially has the width0 over a first axial part, that is to say is an edge, and widens in asecond axial part from 0 up to the shearing flight width of the middlepiece of the shearing flight 7.

FIG. 3 shows the screw element according to the invention in a sideview. Over the axial length 1, this screw element is divided into parts,the axial lengths of which are identified by the letters a-g. In thechosen exemplary embodiment, the axial lengths of the parts a and g, band f, c and e are the same as one another in pairs. A total of 7sections, which are denoted by the letters IV—IV to X—X, have been takenthrough the individual parts, in each case transversely with respect tothe longitudinal axis 10. These 7 sections are specifically representedin FIGS. 4 to 10. Comparable salient points of the cross sections arerespectively identified by P and a consistent numerical index. Todifferentiate the individual sections, the numerical index issupplemented by an additional lower-case letter (for example a)corresponding to the respective section. By comparison of the individualsections, the profiles of the flight elements, which are likewisespecified in a way corresponding to the identification from FIGS. 1-3,can be specifically followed. Table 1 provides the particulars ofparameters for the individual arcs of circles in relation to each of the7 profile sections (corner points, radius, center point), from which theprofile sections IV—IV to X—X are respectively made up, so that it ispossible to dispense with a detailed verbal description.

FIG. 3 shows the screw element according to the invention in a sideview. Over the axial length 1, this screw element is divided into parts,the axial lengths of which are identified by the letters a-g. In thechosen exemplary embodiment, the axial lengths of the parts a and g, band f, c and e are the same as one another in pairs. A total of 7sections, which are denoted by the letters IV—IV to X—X, have been takenthrough the individual parts, in each case transversely with respect tothe longitudinal axis 10. These 7 sections are specifically representedin FIGS. 4 to 10. Comparable salient points of the cross sections arerespectively identified by P and a consistent numerical index. Todifferentiate the individual sections, the numerical index issupplemented by an additional lower-case letter (for example a)corresponding to the respective section (for example IV—IV). Bycomparison of the individual sections, the profiles of the flightelements, which are likewise specified in a way corresponding to theidentification from FIGS. 1-3, can be specifically followed. Table 1provides the particulars of parameters for the individual arcs ofcircles in relation to each of the 7 profile sections (corner points,radius, center point), from which the profile sections IV—IV to X—X arerespectively made up, so that it is possible to dispense with a detailedverbal description.

In FIG. 4 the radii of four circles important for the design have beenentered, that is the outer radius R_(a), the shearing flight radiusR_(s), the core radius R_(i), and a radius R_(i)+R_(a)−R_(s).Furthermore, the flight land angle φ of the shearing flight 1 isindicated. The angle α denotes the angle by which the right flight edge6 is turned about the longitudinal axis 10 (=center point of therespective profile section) with respect to the vertical. However, thisangle α has no influence on the design of the profile cross section. βdenotes the angle of torsion of the shearing flight 7, which is thatangle by which, seen in cross section, the right flight edge of theshearing flight 7, which respectively bears the point designation P₃(that is to say P_(3a)-P_(3g)), is turned with respect to the rightflight edge 6 or 6′ about the longitudinal axis 10. In table 2, thevalue which the angle β has at the start (start limiting angle) and atthe end (end limiting angle) of the respective profile portion isentered for each of the profile portions a-g defined according to FIG.3. Within the respective profile portion, the angle β changescontinuously between these two limiting angles. In addition, it is alsoindicated in table 2 for each profile portion which value the shearingflight land angle δ respectively has in these profile portions. In theprofile portions a and g, the angle δ is in each case constantly equalto 0°, i.e. the shearing flight width is 0 (edge). In the profileportions c, d and e, the shearing flight land angle is in each case atthe value δ_(set), i.e. there is a constant shearing flight width. Inthe two portions b and f, the shearing flight width or the shearingflight land angle δ respectively increases continuously from 0° to thedesired value δ_(set) and decreases from this value δ_(set) down to 0.

FIGS. 4 to 6 show that the width of the flight 1 lying between thepoints P₇ and P₁ significantly decreases from the section IV—IV to thesection VI—VI. In FIG. 7, the flight 1 is no longer present and all thatremains to be seen is the edge 11 originating from it, on which thepoint P₁ (P_(1d)) continues to progress (FIGS. 8-10) in the form of thepoints P_(1e) to P_(1g), until finally, at the rear end face 8′, itcoincides with the rear right flight edge 6′ (FIG. 3). The samecorrespondingly applies to the flight 1′, which is bounded at the rearend face 8′ by the two flight edges 5′ and 6′ if the FIGS. 4 to 10 areconsidered in reverse sequence and the progression of the points P₁₀(P_(10g),P_(10f)) and P₆(P_(6g)-P_(6a)) is followed.

With regard to the shearing flight 7, the following can be stated: inFIG. 4, the shearing flight can only be seen in the unsectioned rearpart of the flight element. In section IV—IV, the width of the shearingflight 7 is zero, that is to say it is represented only as an edge atthe point P_(3a). In the next figure, FIG. 5, the shearing flight 7 hasalready reached approximately half its setpoint value, which isindicated by the shearing flight land angle δ and is also revealed bythe side view of the profile portion b in FIG. 3. The section VI—VI inFIG. 3 shows the shearing flight 7 with its full setpoint width, whichextends between the points P_(2c) and P_(3c). This setpoint width of theshearing flight 7 also lies in the next two sections VII—VII (FIG. 7)and VII—VII (FIG. 8). In FIG. 9 (section IX—IX), the two points P₂ andP₃ move closer together again, i.e. the width of the shearing flight 7in the form of the shearing flight land angle δ decreases again. To thisextent, FIG. 9 corresponds to the representation in FIG. 5. In FIG. 10,the shearing flight 7 has again been reduced to an edge, which isrepresented by the point P_(2g). To this extent, FIG. 10 corresponds tothe representation of FIG. 4. Insofar as the individual profile pointsP₁ to P₁₂ from FIGS. 4 to 10 can be seen in the side view of FIG. 3,they have been entered there.

In FIGS. 11 and 12, a modification of the screw element according toFIGS. 1-3 is represented from the front left and front right,respectively (in FIG. 11 a as a wire model and in FIG. 12 as a surfacemodel). This differs only in that an additional pitch has beensuperposed on the screw element. In the present example, this additionalpitch corresponds to a twisting by turning the profile of the rear endface 8′ with respect to the front end face 8 through a turning angle of360° counter to the intended direction of rotation of the screw profile(that is to say turning to the left). In the present case, the twistingof the profile cross section was performed uniformly over the entireaxial length of the screw profile. As a result, the right flight edge nolonger runs parallel to the longitudinal axis 10, as in FIG. 3, butturns with a left twist about the longitudinal axis 10. The left flightedge 5 no longer turns about the longitudinal axis 10 with a righttwist, as in FIG. 2, but likewise with a left twist. The samecorrespondingly applies to the edge 11, in which the left and rightflight edges 5, 6 continue. Furthermore, FIG. 11 shows the profile ofthe shearing flight 7, which no longer turns through more than 180° in aright-turning sense about the longitudinal axis 10, but now in aleft-turning sense over an angle of less than 180° from the flank 4 fromthe proximity of the right flight edge 6 of the front end face to theleft flank 3′ into the proximity of the left flight edge 5′ of the rearend face 8′.

In the present exemplary embodiment, a linear change of the angle β isrespectively taken as a basis, that is to say a change which isproportional to the respective axial distance of a profile section fromthe front end face. It goes without saying that it is also possible toestablish a different kind of changing increase of the angle β as afunction of the axial length. The same correspondingly also applies tothe increase of the angle δ from 0° to the desired setpoint value. Withrespect to the latter, it should be noted that this setpoint value, thatis to say the shearing flight width in the axial middle region of thescrew element, does not necessarily have to be strictly constant. Aconstant shearing flight width means a constant shearing magnitude overthe axial length of the shearing flight.

TABLE 1 Profile sections Parameter specification to the circular arcs ofthe profile sections IV-IV Endpoints P_(1a), P_(3a) P_(3a), P_(4a)P_(4a), P_(5a) P_(5a), P_(6a) P_(6a), P_(7a) P_(7a), P_(1a) RadiusR_(a) + R_(i) R_(a) + R_(i) R_(i) R_(a) + R_(i) R_(a) + R_(i) R_(a)Midpoint P_(6a) P_(7a) 10 P_(1a) P_(3a) 10 V-V Endpoints P_(1b), P_(2b)P_(2b), P_(3b) P_(3b), P_(4b) P_(4b), P_(5b) P_(5b), P_(6b) P_(6b),P_(8b) P_(8b), P_(7b) P_(7b), P_(1b) Radius R_(a) + R_(i) R_(S) R_(a) +R_(i) R_(i) R_(a) + R_(i) R_(i) + R_(a) − R_(S) R_(a) + R_(i) R_(a)Midpoint P_(6b) 10 P_(7b) 10 P_(1b) 10 P_(3b) 10 VI-VI Endpoints P_(1c),P_(2c) P_(2c), P_(3c) P_(3c), P_(4c) P_(4c), P_(5c) P_(5c), P_(6c)P_(6c), P_(9c) P_(9c), P_(8c) P_(8c), P_(7c) P_(7c), P_(1c) RadiusR_(a) + R_(i) R_(S) R_(a) + R_(i) R_(i) R_(a) + R_(i) R_(a) + R_(i)R_(i) + R_(a) − R_(S) R_(a) + R_(i) R_(a) Midpoint P_(6c) 10 P_(7c) 10P_(1c) P_(2c) 10 P_(3c) 10 VII-VII Endpoints P_(1d), P_(2d) P_(2d),P_(3d) P_(3d), P_(6d) P_(6d), P_(9d) P_(9d), P_(8d) P_(8d), P_(1d)Radius R_(a) + R_(i) R_(S) R_(a) + R_(i) R_(a) + R_(i) R_(i) + R_(a) −R_(S) R_(a) + R_(i) Midpoint P_(6d) 10 P_(1d) P_(2d) 10 P_(3d) VIII-VIIIEndpoints P_(1e), P_(11e) P_(11e), P_(12e) P_(12e), P_(2e) P_(2e),P_(3e) P_(3e), P_(6e) P_(6e), P_(10e) P_(10e), P_(9e) P_(9e), P_(8e)P_(8e), P_(1e) Radius R_(a) + R_(i) R_(i) R_(a) + R_(i) R_(S) R_(a) +R_(i) R_(a) R_(a) + R_(i) R_(i) + R_(a) − R_(S) R_(a) + R_(i) MidpointP_(6e) 10 P_(10e) 10 P_(1e) 10 P_(2e) 10 P_(3e) IX-IX Endpoints P_(1f),P_(11f) P_(11f), P_(12f) P_(12f), P_(2f) P_(2f), P_(3f) P_(3f), P_(6f)P_(6f), P_(10f) P_(10f), P_(9f) P_(9f), P_(1f) Radius R_(a) + R_(i)R_(i) R_(a) + R_(i) R_(S) R_(a) + R_(i) R_(a) R_(a) + R_(i) R_(i) +R_(a) − R_(S) Midpoint P_(6f) 10 P_(10f) 10 P_(1f) 10 P₂f 10 X-XEndpoints P_(1g), P_(11g) P_(11g), P_(12f) P_(12g), P_(2g) P_(2g),P_(6g) P_(6g), P_(10g) P_(10g), P_(1g) Radius R_(a) + R_(i) R_(i)R_(a) + R_(i) R_(a) + R_(i) R_(a) R_(a) + R_(i) Midpoint P_(6g) 10P_(10g) P_(1g) 10 P_(2g)

TABLE 2 Profile section Start limiting angle End limiting angle a δ = 0°δ = 0° Section IV-IV$\beta = {\arccos\quad{\left( \frac{{Ra}^{2} + {Rs}^{2} - \left( {{Ri} + {Ra}} \right)^{2}}{2{RaRs}} \right) \cdot \arccos}\quad\left( {1 - \frac{\left( {{Ri} + {Ra}} \right)^{2}}{2{Ra}^{2}}} \right)}$$\beta = {180{{^\circ} \cdot \arccos}\quad\left( \frac{\left( {{Ri} + {Ra}} \right)^{2} - {Ra}^{2} - \left( {{Ri} + {Ra} - {Rs}} \right)^{2}}{{- 2}{{Ra}\left( {{Ri} + {Ra} - {Rs}} \right)}} \right)}$b δ = 0° δ = δ_(Soll) Section V-V$\beta = {180{{^\circ} \cdot \arccos}\quad\left( \frac{\left( {{Ri} + {Ra}} \right)^{2} - {Ra}^{2} - \left( {{Ri} + {Ra} - {Rs}} \right)^{2}}{{- 2}{{Ra}\left( {{Ri} + {Ra} - {Rs}} \right)}} \right)}$$\beta = {{180{{^\circ} \cdot \arccos}\quad\left( \frac{\left( {{Ri} + {Ra}} \right)^{2} - {Ra}^{2} - \left( {{Ri} + {Ra} - {Rs}} \right)^{2}}{{- 2}{{Ra}\left( {{Ri} + {Ra} - {Rs}} \right)}} \right)} + \delta_{Soll}}$c δ = δ_(Soll) δ = δ_(Soll) Section VI-VI$\beta = {{180{{^\circ} \cdot \arccos}\quad\left( \frac{\left( {{Ri} + {Ra}} \right)^{2} - {Ra}^{2} - \left( {{Ri} + {Ra} - {Rs}} \right)^{2}}{{- 2}{{Ra}\left( {{Ri} + {Ra} - {Rs}} \right)}} \right)} + \delta_{Soll}}$β = arccos ((Ra² + Rs² − (Ri + Ra)²)/(2RaRs)) d δ = δ_(Soll) δ =δ_(Soll) Section VII-VII β = arccos ((Ra² + Rs² − (Ri + Ra)²)/(2RaRs))$\begin{matrix}{\beta = {{360{{^\circ} \cdot \arccos}\quad\left( \frac{{2{Ra}^{2}} - \left( {{Ri} + {Ra}} \right)^{2}}{2{Ra}^{2}} \right)} -}} \\{{\arccos\quad\left( \frac{{Ra}^{2} + {Rs}^{2} - \left( {{Ri} + {Ra}} \right)^{2}}{2{RaRs}} \right)} + \delta_{soll}}\end{matrix}\quad$ e δ = δ_(Soll) δ = δ_(Soll) Section VIII-VIII$\begin{matrix}{\beta = {{360{{^\circ} \cdot \arccos}\quad\left( \frac{{2{Ra}^{2}} - \left( {{Ri} + {Ra}} \right)^{2}}{2{Ra}^{2}} \right)} -}} \\{{\arccos\quad\left( \frac{{Ra}^{2} + {Rs}^{2} - \left( {{Ri} + {Ra}} \right)^{2}}{2{RaRs}} \right)} + \delta_{soll}}\end{matrix}\quad$ $\begin{matrix}{\beta = {{180{{^\circ} \cdot \arccos}\quad\left( \frac{{Ra}^{2} - \left( {{Ri} + {Ra} - {Rs}} \right)^{2} - \left( {{Ri} + {Ra}} \right)^{2}}{2{{Ra}\left( {{Ri} + {Ra} - {Rs}} \right)}} \right)} -}} \\{\arccos\quad\left( \frac{{2{Ra}^{2}} - \left( {{Ri} + {Ra}} \right)^{2}}{2{Ra}^{2}} \right)}\end{matrix}\quad$ f δ = δ_(Soll) δ = 0° Section IX-IX $\begin{matrix}{\beta = {{180{{^\circ} \cdot \arccos}\quad\left( \frac{{Ra}^{2} - \left( {{Ri} + {Ra} - {Rs}} \right)^{2} - \left( {{Ri} + {Ra}} \right)^{2}}{2{{Ra}\left( {{Ri} + {Ra} - {Rs}} \right)}} \right)} -}} \\{\arccos\quad\left( \frac{{2{Ra}^{2}} - \left( {{Ri} + {Ra}} \right)^{2}}{2{Ra}^{2}} \right)}\end{matrix}\quad$ $\begin{matrix}{\beta = {{180{{^\circ} \cdot \arccos}\quad\left( \frac{{Ra}^{2} - \left( {{Ri} + {Ra} - {Rs}} \right)^{2} - \left( {{Ri} + {Ra}} \right)^{2}}{2{{Ra}\left( {{Ri} + {Ra} - {Rs}} \right)}} \right)} -}} \\{\arccos\quad\left( \frac{{2{Ra}^{2}} - \left( {{Ri} + {Ra}} \right)^{2}}{2{Ra}^{2}} \right)}\end{matrix}\quad$ g δ 0° δ = 0° Section X-X $\begin{matrix}{\beta = {{180{{^\circ} \cdot \arccos}\quad\left( \frac{{Ra}^{2} - \left( {{Ri} + {Ra} - {Rs}} \right)^{2} - \left( {{Ri} + {Ra}} \right)^{2}}{2{{Ra}\left( {{Ri} + {Ra} - {Rs}} \right)}} \right)} -}} \\{\arccos\quad\left( \frac{{2{Ra}^{2}} - \left( {{Ri} + {Ra}} \right)^{2}}{2{Ra}^{2}} \right)}\end{matrix}\quad$ $\begin{matrix}{{\beta = {360{{^\circ} \cdot \arccos}\quad{\left( \frac{{2{Ra}^{2}} - \left( {{Ri} + {Ra}} \right)^{2}}{2{Ra}^{2}} \right) \cdot}}}\quad} \\{{\arccos\left( \frac{{Ra}^{2} + {Rs}^{2} - \left( {{Ri} + {Ra}} \right)^{2}}{2{RaRs}} \right)} +} \\{\arccos\quad\left( {1 - \frac{\left( {{Ri} + {Ra}} \right)^{2}}{2{Ra}^{2}}} \right)}\end{matrix}\quad$

1. A screw element for multiscrew extruders with co-rotating andintermeshing screw shafts, said screw element having an outer radius anda core radius and being rotatable about a longitudinal axis in adirection of rotation, the outer radius being greater than the coreradius, the screw element further having an axial length and front andrear end faces at axial ends thereof, a profile of said screw element inaxial cross-section at each of said front and rear end faces has onlyone screw flight, the screw flight at each of said front and rear endfaces having left and right edges defining a flight surface therebetweencomprising a section of a cylindrical surface having the outer radius,the profile of said screw element at each of said front and rear endfaces having a circular root with the core radius and left and rightflanks which join the root to the left and right flight edges,respectively, wherein said flight surface at said front end facecomprises a circumferential width that, proceeding from the front endface for a partial length of said axial length along said longitudinalaxis, decreases to zero, one of said left and right edges of said flightsurface at said front end face meeting a first common edge at saidpartial length, said first common edge proceeding to said rear end face,wherein a distance of said first common edge from said longitudinal axisfirst decreases and then increases proceeding from the end of saidpartial length to said rear end face along said longitudinal axis, saidfirst common edge ending at one of the left and right flight edges ofthe flight surface at the rear end face that faces the direction ofrotation, said flight surface at said rear end face comprises acircumferential width that, proceeding from the rear end face for thepartial length along said longitudinal axis, decreases to zero, one ofsaid left and right edges of said flight surface at said rear end facemeeting a second common edge at said partial length, said second commonedge proceeding to said front end face, wherein a distance of saidsecond common edge from said longitudinal axis first decreases and thenincreases proceeding from the end of said partial length to said frontend face along said longitudinal axis, said first common edge ending atone of the left and right flight edges of the flight surface at thefront end face that faces the direction of rotation, and said screwelement further defines a shearing flight having a constant shear radiusthat is greater than the core radius and less than the outer radius,said shear flight proceeding helically in the direction of rotation fromone of said right and left flanks at said front end face that faces thedirection of rotation to one of the right and left flanks at the rearend face that faces away from the direction of rotation, said shearingflight comprising a middle section and two end sections along an axiallength thereof, said middle section having a substantially constantflight width, said end sections comprise transitional sections having awidths which decrease to zero at the front and rear end faces.
 2. Thescrew element of claim 1, wherein the profile of said screw element isdesigned for close meshing with another screw element.
 3. A screwelement in claim 2, wherein an additional pitch is superposed on thescrew element by cross-sectional twisting over at least a portion ofsaid axial length.
 4. The screw element of claim 3, wherein theadditional pitch is produced by twisting the cross-section of screwelement relative to said front end face in the direction of rotation. 5.The screw element of claim 4, wherein the additional pitch is superposedover the entire axial length of said screw element.
 6. The screw elementof claim 4, wherein different additional pitches are superposed on aplurality of axial portions of said axial length.
 7. The screw elementof claim 3, wherein the additional pitch is produced by twisting thecross-section of screw element relative to said front end face in adirection opposing the direction of rotation.
 8. The screw element ofclaim 7, wherein the additional pitch is superposed over the entireaxial length of said screw element.
 9. The screw element of claim 7,wherein different additional pitches are superposed on a plurality ofaxial portions of said axial length.
 10. The screw element of claim 1,wherein the screw element is for a twin screw extruder.